Light from two coherent sources of same amplitude and same wavelength illuminates the screen. The intensity of the central maximum is I. If the sources were noncoherent, the intensity at the same point will be

Options

A. `I"/"2`
B. `I`
C. `I"/"sqrt(2)`
D. `3I"/"4`

Answer

To solve the problem, we need to determine the intensity at a point on the screen when light from two non-coherent sources is used, given that the intensity from two coherent sources at the same point is \( I \).

### Step-by-Step Solution:

1. **Understanding Coherent Sources**:
- When light from two coherent sources of the same amplitude and wavelength interferes, the intensity at the central maximum is given by:
\[ I_c = (A_1 + A_2)^2 \]
where \( A_1 \) and \( A_2 \) are the amplitudes of the two sources.

2. **Intensity of Coherent Sources**:
- Since the sources are coherent and have the same amplitude, we can denote the amplitude as \( A \). Therefore, the intensity at the central maximum becomes:
\[ I_c = (A + A)^2 = (2A)^2 = 4A^2 \]
- Given that the intensity of the central maximum is \( I \), we have:
\[ I = 4A^2 \]

3. **Finding Amplitude**:
- From the equation \( I = 4A^2 \), we can express \( A^2 \) as:
\[ A^2 = \frac{I}{4} \]

4. **Intensity of Non-Coherent Sources**:
- For non-coherent sources, the intensities simply add up without interference effects. Thus, if both sources have the same intensity \( I' \), the total intensity at the same point is:
\[ I' + I' = 2I' \]

5. **Relating Non-Coherent Intensity to Coherent Intensity**:
- Since the coherent sources had an amplitude \( A \), the intensity of each coherent source is:
\[ I' = A^2 = \frac{I}{4} \]
- Therefore, substituting \( I' \) into the equation for non-coherent sources gives:
\[ I_{non-coherent} = 2I' = 2 \left(\frac{I}{4}\right) = \frac{I}{2} \]

6. **Final Result**:
- Hence, the intensity at the same point when the sources are non-coherent is:
\[ I_{non-coherent} = \frac{I}{2} \]

### Conclusion:
The intensity at the same point when the sources are non-coherent is \( \frac{I}{2} \).